Pore-Scale Modeling of Non-Newtonian Flow in Porous Media

Abstract

The thesis investigates the flow of non-Newtonian fluids in porous media using network modeling. Non-Newtonian fluids occur in diverse natural and synthetic forms and have many important applications including in the oil industry. They show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent in which strain rate solely depends on the instantaneous stress, time-dependent in which strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. The methodology followed in this investigation is pore-scale network modeling. Two three-dimensional topologically-disordered networks representing a sand pack and Berea sandstone were used. The networks are built from topologicallyequivalent three-dimensional voxel images of the pore space with the pore sizes, shapes and connectivity reflecting the real medium. Pores and throats are modeled as having triangular, square or circular cross-section by assigning a shape factor, which is the ratio of the area to the perimeter squared and is obtained from the pore space description. An iterative numerical technique is used to solve the pressure field and obtain the total volumetric flow rate and apparent viscosity. In some cases, analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each throat to simulate the flow in the pore space. The time-independent category of the non-Newtonian fluids is investigated using two time-independent fluid models: Ellis and Herschel-Bulkley. Thorough comparison between the two random networks and the uniform bundle-of-tubes model